d by a train of wagons
covering the span. Waddell's tons are short tons of 2000 lb.

ii. _Impact._--If a vertical load is imposed suddenly, but without
velocity, work is done during deflection, and the deformation and stress
are momentarily double those due to the same load at rest on the structure.
No load of exactly this kind is ever applied to a bridge. But if a load is
so applied that the deflection increases with speed, the stress is greater
than that due to a very gradually applied load, and vibrations about a mean
position are set up. The rails not being absolutely straight and smooth,
centrifugal and lurching actions occur which alter the distribution of the
loading. Again, rapidly changing forces, due to the moving parts of the
engine which are unbalanced vertically, act on the bridge; and, lastly,
inequalities of level at the rail ends give rise to shocks. For all these
reasons the stresses due to the live load are greater than those due to the
same load resting quietly on the bridge. This increment is larger on the
flooring girders than on the main ones, and on short main girders than on
long ones. The impact stresses depend so much on local conditions that it
is difficult to fix what allowance should be made. E.H. Stone (_Trans. Am.
Soc. of C.E._ xli. p. 467) collated some measurements of deflection taken
during official trials of Indian bridges, and found the increment of
deflection due to impact to depend on the ratio of dead to live load. By
plotting and averaging he obtained the following results:--

_Excess of Deflection and straining Action of a moving Load over that due
to a resting Load._

Dead load in per cent | | | | | | | |
of total load .... | 10 | 20 | 30 | 40 | 50 | 70 | 90 |
Live load in per cent | | | | | | | |
of total load .... | 90 | 80 | 70 | 60 | 50 | 30 | 10 |
Ratio of live to dead | | | | | | | |
load ............. | 9 | 4 |2.3 |1.5 |1.0 |0.43|0.10|
Excess of deflection | | | | | | | |
and stress due to | | | | | | | |
moving load | | | | | | | |
per cent ......... | 23 | 13 | 8 |5.5 |4.0 |1.6 |0.3 |

These results are for the centre deflections of main girders, but Stone
infers that the augmentation of stress for any member, due to causes
included in impact allowance, will be the same percentage for the same